On the Structure of the Observable Algebra for QED on the Lattice

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We prove that the matter field subalgebra of the observable algebra for QED on a finite lattice is isomorphic to the enveloping algebra of the Lie algebra 𝓈𝓁(2N, ℂ), factorized by a certain ideal. Using this result, we give a new proof of the decomposition of the physical Hilbert space into charge superselection sectors.

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